In reinforcement learning, is the value of terminal/goal state always zero?
In reinforcement learning, is the value of terminal/goal state always zero?

Yes, always for episodic problems, the value of a terminal state is always zero, from the definition.
The value of a state $v(s)$ is the expected sum (perhaps discounted) of rewards from all future time steps. There are no future time steps when in a terminal state, so this sum must be zero.
For the sake of consistent maths notation, you can consider a terminal state to be &quot;absorbing&quot;, i.e. any transition out of it results in zero reward and returning to the same terminal state. Then you can use the definition of value function to show the same thing:
$$v_{\pi}(s) = \mathbb{E}_{\pi}[\sum_{k=0}^{\infty} \gamma^k R_{t+k+1} | S_{t} = s]$$
If $s = s_T$, the terminal state, then all the &quot;future rewards&quot; from $k=0$ onwards starting with reward $R_{t+1}$ must be zero. This is consistent with the reward $R_{t}$, i.e. the reward when transitioning to the terminal state, being any value.
You can show similar using action value functions, if you accept a &quot;null&quot; action in the terminal state.